The Fourier transform spectrometer (FTS) is a precision infrared detection instrument. It adopts Michelson interference splitting, and the moving mirror is one of the core components. The uniformity and stability of the moving mirror’s speed directly affect the quality of the subsequent interferogram, so it is necessary to carry out high-precision motion control of the moving mirror. For some FTS with moving mirror in low-speed motion, the traditional M-method can no longer meet the requirements of speed measurement accuracy. In addition, when the moving mirror moves at a low speed, the speed stability is more easily affected by external mechanical disturbance. Based on the stability requirement of the low-speed moving mirror, this paper studies the motion control of the moving mirror based on the T-method measuring speed. It proposes a high-precision algorithm to obtain the measured and expected value of the velocity. By establishing the mathematical model and dynamic equation of the controlled object, the speed feedforward input is obtained, and then the compound speed controller based on the feedforward control is designed. The control algorithm is implemented by the FPGA hardware platform and applied to the FTS. The experimental results show that the error of the peak-to-peak velocity is 0.0182, and the error of the root mean square (RMS) velocity is 0.0027. To test the anti-interference ability of the moving mirror speed control system, 5mg sine excitation force is applied in the motion direction of the moving mirror on the FTS for frequency-fixed scanning. The frequency range is 2-200Hz. The experimental results show that under the excitation, the maximum error of the peak-to-peak velocity is 0.0679, and the maximum error of the RMS velocity is 0.0205. The speed stability of the moving mirror can still meet the performance requirements of the FTS. This design provides a technical means for realizing the speed control of the moving mirror with low speed and high stability. Also it makes the FTS have wider applications.